Adaptive harvest management for eastern mallards 1999 progress report

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U. S. Fish & Wildlife Service
Adaptive
Harvest Management
for Eastern Mallards
1999 Progress Report
AHM for Eastern Mallards Page 2
Adaptive Harvest Management for Eastern Mallards
1999 Progress Report
Fred A. Johnson
Office of Migratory Bird Management
U.S. Fish & Wildlife Service
Laurel, Maryland
July 25, 1999
Mallards breeding east of the midcontinent survey area (Fig. 1) winter in the Atlantic and Mississippi
Flyways, where they contribute significantly to the sport harvest. Since the 1980's, there has been an
ongoing effort to understand the ecology of these mallards, and to develop a procedure for recognizing this
mallard population in the development of annual hunting regulations. This report provides information
regarding the effort to modify the adaptive harvest management (AHM) protocol to account for mallards
breeding in eastern Canada and the northeastern U.S.1 For purposes of this report, eastern mallards are
defined as those breeding in survey strata 51-54 and 56, and in New Hampshire, Vermont, Massachusetts,
Connecticut, Rhode Island, New York, Pennsylvania, New Jersey, Delaware, Maryland, and Virginia.
In this report I address five questions concerning this effort:
I. Is it important to account for eastern mallards in the AHM process?
II. How will the AHM protocol be modified to account for eastern mallards?
III. What is the status of efforts to predict (model) responses of eastern mallards to harvest and
uncontrolled environmental factors?
IV. What is the status of necessary modifications to the decision-making process?
V. Are there any concerns about this effort?
midcontinent
eastern
Mallard population:
Fig. 1. Survey areas currently assigned to the midcontinent and
eastern populations of mallards for purposes of harvest management.
1 All analyses in this report are based on current information; results are subject to change as new information becomes available.
AHM for Eastern Mallards Page 4
I. Is it important to account for eastern mallards in the AHM
process?
The current AHM protocol explicitly recognizes only a midcontinent population of mallards, which is
defined as those birds breeding in the traditional survey area and in the states of Minnesota, Wisconsin, and
Michigan. Based on population surveys, band-recovery data, hunter surveys, and other information, the
biology of eastern mallards appears to differ from that of midcontinent mallards in several important ways
(Table 1). The midcontinent population is much larger than the eastern population, and population size has
been fairly stable over time. The eastern population appears to be more productive than the midcontinent
population, and apparently has been growing in size at least since the mid-1960's.
These biological differences suggest differences in allowable harvest pressure. Based on current population
models, the optimal regulatory strategy for eastern mallards tends to be more liberal than that for the
midcontinent population, even in the face of regulation-specific harvest rates that are higher in eastern
North America (U.S. Fish and Wildlife Service. 1998. Adaptive harvest management: Considerations for
the 1998 duck hunting season. U.S. Dep. Inter., Washington, D.C. 29pp.). This difference in optimal
regulatory strategies could lead to situations where status of the two populations warranted different
regulations. This presents a fundamental problem because the current AHM protocol permits only one
regulatory alternative to be applied nationwide based on the status of midcontinent mallards.
Table 1. Some differences in the biology of midcontinent and eastern mallards. Standard errors are in
parentheses.
Parameter Midcontinent
mallards
Eastern mallards
abundance (1998) 9.64 (0.30) million 1.04 (0.08) million
annual growth rate -0.010 (0.003) 0.079 (0.002)
natural survival (adult females) 0.638 (0.010) 0.647 (0.009)
natural survival (adult males) 0.814 (0.015) 0.821 (0.006)
young/adult in fall population 0.865 (0.043) 1.711 (0.119)
proportion wintering in Atlantic Flyway 0.025 (0.003) 0.737 (0.072)
proportion wintering in Mississippi Flyway 0.705 (0.050) 0.262 (0.060)
proportion wintering in Central & Pacific Flyways 0.270 (0.021) 0.001 (0.001)
annual precipitation in core breeding range (cm) 41.8 (5.6) 106.4 (14.7)
I examined the potential for conflicting regulatory prescriptions between midcontinent and eastern mallards
using current models of population dynamics. I generated independent optimal strategies for midcontinent
and eastern mallards, assuming that all Flyways would use the same regulatory option. I used the current
set of regulatory alternatives, the current objective for midcontinent mallards, and an objective to maximize
the long-term cumulative harvest of eastern mallards. Upon simulating the two population-specific
AHM for Eastern Mallards Page 5
strategies, I found that the midcontinent population would be managed primarily by the moderate (22% of
years) and liberal (64% of years) options. The eastern population would be managed almost entirely with
the liberal option (98% of years). I assumed that the two populations are independent (no exchange, no
correlation in relevant environmental conditions), and estimated the percentage of years in which there
would be conflicting regulatory prescriptions for the two populations (Table 2). The down diagonal in the
table (shaded) represents the percentage of years in which there would be no conflict in regulatory
prescriptions (about 63%). Above the diagonal represents years in which the eastern population would be
harvested at a rate less than optimal if all Flyways were driven by a midcontinent strategy (about 35%).
Below the diagonal represents years when eastern mallards would be harvested at a rate higher than optimal
(2%).
Based on this analysis, the Atlantic Flyway might expect overly restrictive regulations in about three out of
ten years, if the Flyway’s regulations continued to be determined solely on the basis of midcontinent
mallards. In virtually all of those years, the Atlantic Flyway would experience regulations that were only
one level more restrictive than would be optimal based on the status of eastern mallards (e.g., moderate
instead of liberal).
Table 2. The expected frequency (%) of years with population-specific regulatory choices. VR=very
restrictive, R=restrictive, M=moderate, and L=liberal regulations.
Eastern population
Midcontinent
population
VR R M L
VR 0.0 0.0 0.0 2.1
R 0.0 0.1 0.2 12.2
M 0.0 0.2 0.3 21.0
L 0.0 0.5 1.0 62.4
AHM for Eastern Mallards Page 6
II. How will the AHM protocol be modified to account for eastern
mallards?
Modification of the current AHM protocol to account for the status of eastern mallards involves:
(1) revision of the objective function to account for harvest-management goals for eastern mallards;
(2) augmentation of the decision criteria to include population and environmental variables relevant to
eastern mallards; and
(3) modification of the decision rules to allow Flyway-specific regulatory choices.
Once these modifications are made, there no longer will be a need for two population-specific regulatory
strategies. Essentially, the strategies would be melded into one, where regulatory-decision criteria would
include both population size of midcontinent and eastern mallards, as well as environmental indicators
appropriate for each population (e.g., ponds in southern Canada and spring precipitation in the northeastern
U.S.). Moreover, instead of one regulatory prescription for all Flyways, optimal regulatory choices would
be Flyway-specific based on the relative contribution of the two populations to the respective Flyways.
To demonstrate this framework, I derived an optimal harvest strategy using simplified versions of the
current models of mallard population dynamics (e.g., I assumed all cohorts were equally vulnerable to
harvest). I also assumed that managers have direct and perfect control over harvest rates. I permitted the
Central and Pacific Flyways to share the same harvest rate because their harvests are derived almost
entirely from the midcontinent population. Finally, I used a harvest-management objective to maximize the
long-term cumulative harvest of mallards (regardless of their origin), conditional on maintaining the
midcontinent population above the goal of the North American Waterfowl Management Plan. Table 3
contains excerpts from the full optimal harvest strategy, which is too large to reproduce in its entirety.
Although I emphasize that this table is for demonstration purposes, it does reveal some interesting patterns
of harvest rates. As expected, the optimal harvest rate for the Atlantic Flyway is highly dependent on the
status of eastern mallards (first portion of the table). Also, as expected, optimal harvest rates are positively
related to the status of midcontinent mallards. However, the relationship between Flyway-specific harvest
rates and the status of midcontinent mallards occasionally is counter-intuitive. Although these patterns
could be the result of over-simplifying the mallard models, they may suggest that managers ultimately will
need to specify how the available harvest (and, thus, hunting opportunity) is to be shared (allocated) among
Flyways.
AHM for Eastern Mallards Page 7
Table 3. A portion of an optimal harvest strategy for mallards. See text for information regarding its
derivation.
Optimal harvest rate
Midcontinent
population
Ponds Eastern
population
Spring
precip.
Cen. & Pac.
Flyways
Miss.
Flyway
Atl. Flyway
4.0e+6 4.0e+6 0.50e+6 11 0.00 0.00 0.00
4.0e+6 4.0e+6 0.75e+6 11 0.00 0.00 0.05
4.0e+6 4.0e+6 1.00e+6 11 0.00 0.00 0.25
4.0e+6 4.0e+6 1.25e+6 11 0.00 0.00 0.35
4.0e+6 4.0e+6 1.50e+6 11 0.00 0.00 0.40
… … … … … … …
8.0e+6 1.0e+6 1.00e+6 11 0.30 0.00 0.45
8.0e+6 2.5e+6 1.00e+6 11 0.35 0.00 0.45
8.0e+6 4.0e+6 1.00e+6 11 0.35 0.00 0.45
8.0e+6 5.5e+6 1.00e+6 11 0.10 0.15 0.40
8.0e+6 7.0e+6 1.00e+6 11 0.15 0.15 0.40
… … … … … … …
4.0e+6 5.5e+6 1.00e+6 11 0.00 0.00 0.25
6.0e+6 5.5e+6 1.00e+6 11 0.10 0.00 0.45
8.0e+6 5.5e+6 1.00e+6 11 0.10 0.15 0.40
10.0e+6 5.5e+6 1.00e+6 11 0.30 0.15 0.40
12.0e+6 5.5e+6 1.00e+6 11 0.00 0.35 0.35
AHM for Eastern Mallards Page 8
III. What is the status of efforts to predict (model) responses of
eastern mallards to harvest and uncontrolled environmental factors?
We have made important advances in understanding the dynamics of waterfowl populations and the
impacts of hunting regulations by investigating patterns in abundance data, monitoring harvests, and
estimating key parameters such as survivorship and reproduction. This information is folded into models
of population size and distribution, as influenced by harvest regulations and uncontrolled environmental
factors. By building on the databases they are designed to represent, these population models provide a
predictive tool for management and, thus, represent a critical component of the regulations-setting process.
The formal effort to model population dynamics of eastern mallards began in 1988. Dr. David Gordon
(Ducks Unlimited) was contracted to assemble and summarize relevant monitoring data, and to determine
patterns of mallard derivation within the Flyway. That contract was completed in 1994. In 1995, Dr. Sue
Sheaffer (New York Cooperative Fish & Wildlife Research Unit) was contracted to develop quantitative
models describing the population dynamics of eastern mallards. In 1996, Dr. Sheaffer completed a
comprehensive assessment of reproductive and mortality processes, and suggested a set of alternative
models for use in the AHM framework. In 1997, I relied on Dr. Sheaffer’s work and other anlayses to
develop a single “working model,” because key sources of uncertainty had not been agreed upon, and
because of concern that some of the models had been over-parameterized (i.e., more parameters than
necessary were used to describe population dynamics). This “working model” currently is being used to
assess optimal regulations for eastern mallards, although the status of midcontinent mallards continues to
drive a nationwide regulatory decision.
The working model for eastern mallards predicts population size (N) as measured in the combined federal
and state waterfowl surveys in eastern Canada and the northeastern U.S. However, these surveys have not
been operational long enough to permit estimation of the relationship between abundance and reproductive
rate. Therefore, the model relies on a Breeding Bird Survey (BBS) index, and its empirical relationship to
N, to predict annual reproduction (At) using a logit transformation:
ln
´A
t
1& ´A
t
' a&b(BBSt)%c(PPTt)
where
´A
t
'
At
Amax
and
At
' Amax
e a&b(BBSt)%c(PPTt)
1%e a&b(BBSt)%c(PPTt)
AHM for Eastern Mallards Page 9
and where At = fall age ratio of females in year t,
a = -0.483415, b = -0.284774, c = 0.121664,
Amax = maximum age ratio = 3.0,
BBS = 0.000004656 * Nt, and
PPT = cumulative precipitation in northeastern states during March to May, which is
distributed Normal(10.7, 4.0).
The model assumes complete additivity of hunting mortality, and predicts changes in population size using:
Nt+1 = Nt * f t ,
where
ft = ((1 - sex) * ssf * (SHAFt + A t * (SHYFt + SHYMt) + sex * ssm * SHAMt) * sw ,
and where sex = 0.55 = mean proportion of males in the breeding population,
ssf = 0.71 = summer survival of females,
ssm = 0.90 = summer survival of males,
sw = 0.90 = winter survival,
SHAFt = hunting-season survival of adult females,
SHYFt = hunting-season survival of young females,
SHYMt = hunting-season survival of young males, and
SHAMt = hunting-season survival of adult males.
Hunting-season survival rates are calculated using harvest rates predicted for each regulatory alternative.
Harvest rates are cohort-specific, based on constant vulnerabilities relative to adult males (0.98 for adult
females, 1.45 for young males, and 1.32 for young females). Hunting-season survival rates also account for
a crippling loss of 20 percent.
I examined the validity of this “working model” by comparing its predictions of annual change in population
size with observed changes from the monitoring program (eastern aerial and plot surveys) (Fig. 2). For both
monitoring observations and model predictions, I calculated the annual growth rate as the ratio of successive
population estimates. I estimated the variance of the observed growth rate using the Taylor-series
approximation for the variance of a ratio. I estimated the variance of the predicted growth rate using
simulation, by assuming that observed population size and harvest rate were normally distributed about their
point estimates.
AHM for Eastern Mallards Page 10
Year
1989 1990 1991 1992 1993 1994 1995 1996
Growth rate (%)
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
predicted
observed
Fig. 2. Estimated growth rates and standard error bars as estimated from the monitoring program (observed) and
from the “working model” (predicted) of population dynamics.
Although the confidence limits for the observed and predicted growth rates overlap in all cases, the point
estimates of the model predictions are usually higher than those observed from the monitoring program. It
is unclear whether the source of this bias is in the “working model's�� survival or reproductive process.
This model validation effort demonstrates the importance of considering a set of alternative models that
capture key uncertainties about population dynamics. Future modeling efforts should focus on the
following issues:
Reproduction.--Among eastern mallards, there is a strong negative relationship between fall age ratios and
indices of breeding-population size, suggesting a high degree of density dependence in reproduction. The
nature of this relationship is important because the presence of strong density-dependence in population
growth can lead to very liberal harvest strategies. Therefore, further investigations are needed to help
understand whether the observed relationship actually represents cause and effect. Also, questions remain
about the influence of environmental conditions on reproduction. To date, no weather variables have
explained much of the variation in fall age ratios, and it is unclear whether these results reflect an
insensitivity to weather conditions or a failure to identify the appropriate weather variable(s).
AHM for Eastern Mallards Page 11
The “working model” relies on the empirical relationship between population size and the BBS index to
predict reproductive success. This relationship currently is based on only seven data points, one for each
year in which both the BBS index and N are available. Although the BBS index and N are positively
correlated (P < 0.01), there is considerable uncertainty regarding the slope, intercept, and shape of this
relationship (Fig. 3). By using a combination of optimization and simulation procedures, I determined that
optimal regulations for eastern mallards are very sensitive to the predicted relationship between N and the
BBS index, particularly at low and high population levels. It is therefore essential that this relationship be
monitored and updated as often as possible.
Mallard population size
5.0e+5 7.5e+5 1.0e+6 1.3e+6 1.5e+6
BBS index
0
1
2
3
4
5
6
7
8
9
10
Fig. 3. The relationship between mallard population size and the Breeding Bird Survey (BBS) index. The dotted
line is the least-square regression and the solid lines are 95% confidence intervals for the mean.
Survival.--There is some evidence that female mallards in the eastern population are more vulnerable to
harvest than their midcontinent counterparts. However, it has been difficult to understand the spatial and
temporal patterns (if any) of harvest vulnerability because band-reporting rates for female mallards in
eastern North America are unknown. Until estimates of band-reporting rate are available, managers
perhaps should consider sex-specific harvest vulnerability as a key source of uncertainty in population
models for eastern mallards.
AHM for Eastern Mallards Page 12
IV. What is the status of necessary modifications to the decision-making
process?
Harvest-management objective(s).--The preliminary objective for eastern mallards is to maximize long-term
cumulative harvest. This objective is subject to change once the implications for average population
size, variability in annual regulations, and other performance characteristics are better understood. The
objective for midcontinent mallards is to maximize long-term cumulative harvest, subject to a population
goal of 8.7 million breeding birds. One of the difficulties in modifying the current AHM framework
involves combining the population-specific objectives into one objective function so that an aggregate
harvest strategy can be derived.
I currently am using an objective function which maximizes the aggregate harvest of both populations, but
devalues all regulatory decisions that result in the midcontinent population falling below goal. This
objective function helps ensure that the midcontinent population goal is not sacrificed for the sake of more
eastern mallard harvest. Much work remains, however, to understand the implications of various objective
functions, particularly on Flyway-specific regulations.
Augmentation of the decision criteria.--I have made considerable progress in augmenting the decision
criteria to include population and environmental variables relevant to eastern mallards. A recent
investigation involves the following scenario:
(1) population models which include the “working model” for eastern mallards, and current models
and associated likelihood weights for midcontinent mallards;
(2) explicit consideration of the eastern population when making a regulatory decision (i.e., decision
criteria to include population sizes of both midcontinent & eastern mallards, Canadian ponds, and
spring precipitation in the northeastern U.S.);
(3) one regulatory decision to apply to all Flyways;
(4) the current set of regulatory alternatives;
(5) deterministic harvest rates (i.e., expected mean harvest rates for both populations under the current
regulatory alternatives); and
(6) an objective function that maximizes the combined harvests of midcontinent and eastern mallards,
subject to the population constraint on midcontinent mallards.
The two “decision matrices” for midcontinent and eastern mallards were “blended” into one via an
optimization algorithm developed for this problem. Because the number of decision criteria has been
increased, the optimal strategy can no longer be displayed as a matrix, but must take the form of a table
(Table 4). Although comprehensive patterns of optimal regulations are hard to discern from the small
portion of the strategy reproduced in Table 4, it does appear that population size of eastern mallards and
spring precipitation in the Northeast can modify the nationwide regulatory decision for a given status of
midcontinent mallards. However, the effect is very small, presumably because the midcontinent population
is so numerically dominant.
AHM for Eastern Mallards Page 13
Table 4. Optimal regulations (C = closed, VR = very restrictive, R = restrictive, M = moderate, and L =
liberal) for mallards breeding in central and eastern North America. Only a small portion of the strategy is
contained in the table.
Midcontinent
population
(millions)
Ponds
(millions)
Eastern
population
(millions)
Northeast spring
precipitation
(inches)
Optimal
regulation
5.0 2.5 0.75 7 C
5.0 2.5 0.75 15 C
5.0 2.5 1.25 7 C
5.0 2.5 1.25 15 C
5.0 4..5 0.75 7 C
5.0 4.5 0.75 15 C
5.0 4.5 1.25 7 C
5.0 4.5 1.25 15 VR
6.5 2.5 0.75 7 VR
6.5 2.5 0.75 15 VR
6.5 2.5 1.25 7 VR
6.5 2.5 1.25 15 VR
6.5 4..5 0.75 7 R
6.5 4.5 0.75 15 R
6.5 4.5 1.25 7 R
6.5 4.5 1.25 15 M
8.0 2.5 0.75 7 M
8.0 2.5 0.75 15 M
8.0 2.5 1.25 7 M
8.0 2.5 1.25 15 M
8.0 4..5 0.75 7 L
8.0 4.5 0.75 15 L
8.0 4.5 1.25 7 L
8.0 4.5 1.25 15 L
AHM for Eastern Mallards Page 14
I compared this policy with the midcontinent policy from last year by taking the mean regulation over all
ponds, eastern mallard population sizes, and Northeast spring precipitation amounts for each level of
midcontinent population size (Fig. 4). For population sizes of midcontinent mallards >8.5 million, there is
little difference in regulations, suggesting that the status of eastern mallards has little effect on the
nationwide decision. At those levels, the midcontinent population simply dwarfs the eastern population
and, thus, dominates the choice of regulations. For midcontinent population sizes <6 million, explicit
consideration of eastern mallards will tend to produce more liberal regulations than would be the case with
a strategy focused solely on midcontinent mallards. In fact, for very low midcontinent mallard sizes,
consideration of eastern mallards can prevent a closed season from being the optimal choice. For
midcontinent population sizes between 6 and 8.5 million, the aggregate strategy actually appears to be
slightly more conservative than the strategy based on midcontinent mallards. I am not sure of the reason
for this result, but I suspect the conservative regulations permit more growth in the midcontinent
population, while substituting harvest from the eastern population. Thus, this example demonstrates the
importance of investigating the implications of various combinations of harvest management objectives for
midcontinent and eastern mallards.
Modification of the decision rules.--Modification of the decision rules to allow for Flyway-specific
regulatory choices greatly complicates the optimization procedures. Instead of five possible regulatory
decisions (C, VR, R, M, and L), we have to evaluate 54 = 625 decisions for every possible combination of
midcontinent population size, ponds, eastern population size, and spring precipitation in the Northeast. If
we assume that the Central and Pacific Flyways could share a regulatory decision, the number of decisions
could be reduced to 53 = 125. Although this simplification would be acceptable for now, the Central and
Pacific Flyways will require separate decisions if and when a western population of mallards is adopted.
The additional complexity arising from the expanded decision space will severely strain our computational
abilities. Investigations into computer hardware and software that can handle these large-dimension
problems are ongoing.
Although season length, bag limits, and other regulatory specifications always have been Flyway-specific,
liberalization or restriction of regulations usually has occurred concurrently in all Flyways. Because of this
tradition, our ability to predict harvest rates resulting from various combinations of Flyway-specific
regulatory alternatives is extremely limited. Therefore, it is imperative that we adopt a stable set of
regulatory alternatives, and then use those alternatives long enough to validate harvest rate predictions.
AHM for Eastern Mallards Page 15
Midcontinent population size
4.0e+6 5.0e+6 6.0e+6 7.0e+6 8.0e+6 9.0e+6 1.0e+7 1.1e+7 1.2e+7
Optimal regulation
0
1
2
3
4
midcontinent strategy
aggregate strategy
Fig. 4. Mean regulatory choices (0 = Closed, 1 = Very restrictive, 2 = Restrictive, 3 = Moderate, and 4 =
Liberal) for various levels of midcontinent population size, as based on the 1998 midcontinent mallard strategy
and on an aggregate strategy that also considers that status of eastern mallards.
AHM for Eastern Mallards Page 16
V. Are there any concerns about this effort?
The role of Flyway biologists.--There is a critical need for Flyway biologists to be involved in modeling the
population dynamics of eastern mallards, and in investigating the management implications of various
models and harvest-management objectives. The Office of Migratory Bird Management (MBMO) does not
have the necessary field experience to formulate hypotheses of eastern mallard ecology, nor does it have
adequate staff resources to sustain a unilateral modeling effort. I encourage the Atlantic Flyway Technical
Section to join in a working partnership, similar to the collaboration between MBMO and the Technical
Section's Canada Goose Committee. In that partnership, MBMO staff provide analytical tools and
assistance, but most investigations are conducted by the Canada Goose Committee.
Intermediate steps.--While we are making considerable progress, it is not yet clear when we will be ready
to move from a nationwide harvest strategy based on midcontinent mallards to a Flyway-specific approach
based on both midcontinent and eastern mallards. In the interim, two alternatives have been suggested.
The first involves augmenting the decision criteria to explicitly include population and environmental
variables relevant to eastern mallards, but continuing to permit only one regulatory decision for all
Flyways. The other alternative involves an Atlantic Flyway regulation based solely on eastern mallards,
and a regulatory choice for the other three Flyways based solely on midcontinent mallards. The first
alternative explicitly recognizes that there is a sharing of mallard populations among the Mississippi and
Atlantic Flyways. The second alternative assumes that there is little or no sharing of populations.
Although we know this assumption to be false, I believe this alternative likely poses little biological risk in
terms of mallard populations.
In the end, however, the problem comes down to predicting the harvest rates realized on each population
when Flyways select different regulatory alternatives. Otherwise, we have no basis to develop an optimal
strategy for either population (unless we assume eastern mallards don't go to the Mississippi Flyway, and
midcontinent mallards don't go to the Atlantic). Since there is a sharing of populations among the Flyways,
we must be able to predict these population-specific harvest rates, even if we were to let the Atlantic be
guided solely by the eastern population, and the rest of the country by the midcontinent population. If we
knew the harvest rates for various combinations of Flyway-specific regulations, then we could develop the
full-featured harvest strategy. Thus, we come full circle, and I believe that the first alternative described
above is the only possible intermediate step. However, the management community must judge whether
this intermediate step is necessary or desirable, given that the interim strategy appears to be only
marginally different from that for the midcontinent population.
Other species.--I am concerned that the “working model,” which tends to over-predict population size,
suggests a very liberal harvest strategy. I don't believe it would be prudent to formally adopt this model, or
its associated Flyway-specific strategies, without an explicit consideration of key sources of model
uncertainty, or without considering how the associated harvest strategy may impact the status of species
like black ducks, scaup, or wood ducks.

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U. S. Fish & Wildlife Service
Adaptive
Harvest Management
for Eastern Mallards
1999 Progress Report
AHM for Eastern Mallards Page 2
Adaptive Harvest Management for Eastern Mallards
1999 Progress Report
Fred A. Johnson
Office of Migratory Bird Management
U.S. Fish & Wildlife Service
Laurel, Maryland
July 25, 1999
Mallards breeding east of the midcontinent survey area (Fig. 1) winter in the Atlantic and Mississippi
Flyways, where they contribute significantly to the sport harvest. Since the 1980's, there has been an
ongoing effort to understand the ecology of these mallards, and to develop a procedure for recognizing this
mallard population in the development of annual hunting regulations. This report provides information
regarding the effort to modify the adaptive harvest management (AHM) protocol to account for mallards
breeding in eastern Canada and the northeastern U.S.1 For purposes of this report, eastern mallards are
defined as those breeding in survey strata 51-54 and 56, and in New Hampshire, Vermont, Massachusetts,
Connecticut, Rhode Island, New York, Pennsylvania, New Jersey, Delaware, Maryland, and Virginia.
In this report I address five questions concerning this effort:
I. Is it important to account for eastern mallards in the AHM process?
II. How will the AHM protocol be modified to account for eastern mallards?
III. What is the status of efforts to predict (model) responses of eastern mallards to harvest and
uncontrolled environmental factors?
IV. What is the status of necessary modifications to the decision-making process?
V. Are there any concerns about this effort?
midcontinent
eastern
Mallard population:
Fig. 1. Survey areas currently assigned to the midcontinent and
eastern populations of mallards for purposes of harvest management.
1 All analyses in this report are based on current information; results are subject to change as new information becomes available.
AHM for Eastern Mallards Page 4
I. Is it important to account for eastern mallards in the AHM
process?
The current AHM protocol explicitly recognizes only a midcontinent population of mallards, which is
defined as those birds breeding in the traditional survey area and in the states of Minnesota, Wisconsin, and
Michigan. Based on population surveys, band-recovery data, hunter surveys, and other information, the
biology of eastern mallards appears to differ from that of midcontinent mallards in several important ways
(Table 1). The midcontinent population is much larger than the eastern population, and population size has
been fairly stable over time. The eastern population appears to be more productive than the midcontinent
population, and apparently has been growing in size at least since the mid-1960's.
These biological differences suggest differences in allowable harvest pressure. Based on current population
models, the optimal regulatory strategy for eastern mallards tends to be more liberal than that for the
midcontinent population, even in the face of regulation-specific harvest rates that are higher in eastern
North America (U.S. Fish and Wildlife Service. 1998. Adaptive harvest management: Considerations for
the 1998 duck hunting season. U.S. Dep. Inter., Washington, D.C. 29pp.). This difference in optimal
regulatory strategies could lead to situations where status of the two populations warranted different
regulations. This presents a fundamental problem because the current AHM protocol permits only one
regulatory alternative to be applied nationwide based on the status of midcontinent mallards.
Table 1. Some differences in the biology of midcontinent and eastern mallards. Standard errors are in
parentheses.
Parameter Midcontinent
mallards
Eastern mallards
abundance (1998) 9.64 (0.30) million 1.04 (0.08) million
annual growth rate -0.010 (0.003) 0.079 (0.002)
natural survival (adult females) 0.638 (0.010) 0.647 (0.009)
natural survival (adult males) 0.814 (0.015) 0.821 (0.006)
young/adult in fall population 0.865 (0.043) 1.711 (0.119)
proportion wintering in Atlantic Flyway 0.025 (0.003) 0.737 (0.072)
proportion wintering in Mississippi Flyway 0.705 (0.050) 0.262 (0.060)
proportion wintering in Central & Pacific Flyways 0.270 (0.021) 0.001 (0.001)
annual precipitation in core breeding range (cm) 41.8 (5.6) 106.4 (14.7)
I examined the potential for conflicting regulatory prescriptions between midcontinent and eastern mallards
using current models of population dynamics. I generated independent optimal strategies for midcontinent
and eastern mallards, assuming that all Flyways would use the same regulatory option. I used the current
set of regulatory alternatives, the current objective for midcontinent mallards, and an objective to maximize
the long-term cumulative harvest of eastern mallards. Upon simulating the two population-specific
AHM for Eastern Mallards Page 5
strategies, I found that the midcontinent population would be managed primarily by the moderate (22% of
years) and liberal (64% of years) options. The eastern population would be managed almost entirely with
the liberal option (98% of years). I assumed that the two populations are independent (no exchange, no
correlation in relevant environmental conditions), and estimated the percentage of years in which there
would be conflicting regulatory prescriptions for the two populations (Table 2). The down diagonal in the
table (shaded) represents the percentage of years in which there would be no conflict in regulatory
prescriptions (about 63%). Above the diagonal represents years in which the eastern population would be
harvested at a rate less than optimal if all Flyways were driven by a midcontinent strategy (about 35%).
Below the diagonal represents years when eastern mallards would be harvested at a rate higher than optimal
(2%).
Based on this analysis, the Atlantic Flyway might expect overly restrictive regulations in about three out of
ten years, if the Flyway’s regulations continued to be determined solely on the basis of midcontinent
mallards. In virtually all of those years, the Atlantic Flyway would experience regulations that were only
one level more restrictive than would be optimal based on the status of eastern mallards (e.g., moderate
instead of liberal).
Table 2. The expected frequency (%) of years with population-specific regulatory choices. VR=very
restrictive, R=restrictive, M=moderate, and L=liberal regulations.
Eastern population
Midcontinent
population
VR R M L
VR 0.0 0.0 0.0 2.1
R 0.0 0.1 0.2 12.2
M 0.0 0.2 0.3 21.0
L 0.0 0.5 1.0 62.4
AHM for Eastern Mallards Page 6
II. How will the AHM protocol be modified to account for eastern
mallards?
Modification of the current AHM protocol to account for the status of eastern mallards involves:
(1) revision of the objective function to account for harvest-management goals for eastern mallards;
(2) augmentation of the decision criteria to include population and environmental variables relevant to
eastern mallards; and
(3) modification of the decision rules to allow Flyway-specific regulatory choices.
Once these modifications are made, there no longer will be a need for two population-specific regulatory
strategies. Essentially, the strategies would be melded into one, where regulatory-decision criteria would
include both population size of midcontinent and eastern mallards, as well as environmental indicators
appropriate for each population (e.g., ponds in southern Canada and spring precipitation in the northeastern
U.S.). Moreover, instead of one regulatory prescription for all Flyways, optimal regulatory choices would
be Flyway-specific based on the relative contribution of the two populations to the respective Flyways.
To demonstrate this framework, I derived an optimal harvest strategy using simplified versions of the
current models of mallard population dynamics (e.g., I assumed all cohorts were equally vulnerable to
harvest). I also assumed that managers have direct and perfect control over harvest rates. I permitted the
Central and Pacific Flyways to share the same harvest rate because their harvests are derived almost
entirely from the midcontinent population. Finally, I used a harvest-management objective to maximize the
long-term cumulative harvest of mallards (regardless of their origin), conditional on maintaining the
midcontinent population above the goal of the North American Waterfowl Management Plan. Table 3
contains excerpts from the full optimal harvest strategy, which is too large to reproduce in its entirety.
Although I emphasize that this table is for demonstration purposes, it does reveal some interesting patterns
of harvest rates. As expected, the optimal harvest rate for the Atlantic Flyway is highly dependent on the
status of eastern mallards (first portion of the table). Also, as expected, optimal harvest rates are positively
related to the status of midcontinent mallards. However, the relationship between Flyway-specific harvest
rates and the status of midcontinent mallards occasionally is counter-intuitive. Although these patterns
could be the result of over-simplifying the mallard models, they may suggest that managers ultimately will
need to specify how the available harvest (and, thus, hunting opportunity) is to be shared (allocated) among
Flyways.
AHM for Eastern Mallards Page 7
Table 3. A portion of an optimal harvest strategy for mallards. See text for information regarding its
derivation.
Optimal harvest rate
Midcontinent
population
Ponds Eastern
population
Spring
precip.
Cen. & Pac.
Flyways
Miss.
Flyway
Atl. Flyway
4.0e+6 4.0e+6 0.50e+6 11 0.00 0.00 0.00
4.0e+6 4.0e+6 0.75e+6 11 0.00 0.00 0.05
4.0e+6 4.0e+6 1.00e+6 11 0.00 0.00 0.25
4.0e+6 4.0e+6 1.25e+6 11 0.00 0.00 0.35
4.0e+6 4.0e+6 1.50e+6 11 0.00 0.00 0.40
… … … … … … …
8.0e+6 1.0e+6 1.00e+6 11 0.30 0.00 0.45
8.0e+6 2.5e+6 1.00e+6 11 0.35 0.00 0.45
8.0e+6 4.0e+6 1.00e+6 11 0.35 0.00 0.45
8.0e+6 5.5e+6 1.00e+6 11 0.10 0.15 0.40
8.0e+6 7.0e+6 1.00e+6 11 0.15 0.15 0.40
… … … … … … …
4.0e+6 5.5e+6 1.00e+6 11 0.00 0.00 0.25
6.0e+6 5.5e+6 1.00e+6 11 0.10 0.00 0.45
8.0e+6 5.5e+6 1.00e+6 11 0.10 0.15 0.40
10.0e+6 5.5e+6 1.00e+6 11 0.30 0.15 0.40
12.0e+6 5.5e+6 1.00e+6 11 0.00 0.35 0.35
AHM for Eastern Mallards Page 8
III. What is the status of efforts to predict (model) responses of
eastern mallards to harvest and uncontrolled environmental factors?
We have made important advances in understanding the dynamics of waterfowl populations and the
impacts of hunting regulations by investigating patterns in abundance data, monitoring harvests, and
estimating key parameters such as survivorship and reproduction. This information is folded into models
of population size and distribution, as influenced by harvest regulations and uncontrolled environmental
factors. By building on the databases they are designed to represent, these population models provide a
predictive tool for management and, thus, represent a critical component of the regulations-setting process.
The formal effort to model population dynamics of eastern mallards began in 1988. Dr. David Gordon
(Ducks Unlimited) was contracted to assemble and summarize relevant monitoring data, and to determine
patterns of mallard derivation within the Flyway. That contract was completed in 1994. In 1995, Dr. Sue
Sheaffer (New York Cooperative Fish & Wildlife Research Unit) was contracted to develop quantitative
models describing the population dynamics of eastern mallards. In 1996, Dr. Sheaffer completed a
comprehensive assessment of reproductive and mortality processes, and suggested a set of alternative
models for use in the AHM framework. In 1997, I relied on Dr. Sheaffer’s work and other anlayses to
develop a single “working model,” because key sources of uncertainty had not been agreed upon, and
because of concern that some of the models had been over-parameterized (i.e., more parameters than
necessary were used to describe population dynamics). This “working model” currently is being used to
assess optimal regulations for eastern mallards, although the status of midcontinent mallards continues to
drive a nationwide regulatory decision.
The working model for eastern mallards predicts population size (N) as measured in the combined federal
and state waterfowl surveys in eastern Canada and the northeastern U.S. However, these surveys have not
been operational long enough to permit estimation of the relationship between abundance and reproductive
rate. Therefore, the model relies on a Breeding Bird Survey (BBS) index, and its empirical relationship to
N, to predict annual reproduction (At) using a logit transformation:
ln
´A
t
1& ´A
t
' a&b(BBSt)%c(PPTt)
where
´A
t
'
At
Amax
and
At
' Amax
e a&b(BBSt)%c(PPTt)
1%e a&b(BBSt)%c(PPTt)
AHM for Eastern Mallards Page 9
and where At = fall age ratio of females in year t,
a = -0.483415, b = -0.284774, c = 0.121664,
Amax = maximum age ratio = 3.0,
BBS = 0.000004656 * Nt, and
PPT = cumulative precipitation in northeastern states during March to May, which is
distributed Normal(10.7, 4.0).
The model assumes complete additivity of hunting mortality, and predicts changes in population size using:
Nt+1 = Nt * f t ,
where
ft = ((1 - sex) * ssf * (SHAFt + A t * (SHYFt + SHYMt) + sex * ssm * SHAMt) * sw ,
and where sex = 0.55 = mean proportion of males in the breeding population,
ssf = 0.71 = summer survival of females,
ssm = 0.90 = summer survival of males,
sw = 0.90 = winter survival,
SHAFt = hunting-season survival of adult females,
SHYFt = hunting-season survival of young females,
SHYMt = hunting-season survival of young males, and
SHAMt = hunting-season survival of adult males.
Hunting-season survival rates are calculated using harvest rates predicted for each regulatory alternative.
Harvest rates are cohort-specific, based on constant vulnerabilities relative to adult males (0.98 for adult
females, 1.45 for young males, and 1.32 for young females). Hunting-season survival rates also account for
a crippling loss of 20 percent.
I examined the validity of this “working model” by comparing its predictions of annual change in population
size with observed changes from the monitoring program (eastern aerial and plot surveys) (Fig. 2). For both
monitoring observations and model predictions, I calculated the annual growth rate as the ratio of successive
population estimates. I estimated the variance of the observed growth rate using the Taylor-series
approximation for the variance of a ratio. I estimated the variance of the predicted growth rate using
simulation, by assuming that observed population size and harvest rate were normally distributed about their
point estimates.
AHM for Eastern Mallards Page 10
Year
1989 1990 1991 1992 1993 1994 1995 1996
Growth rate (%)
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
predicted
observed
Fig. 2. Estimated growth rates and standard error bars as estimated from the monitoring program (observed) and
from the “working model” (predicted) of population dynamics.
Although the confidence limits for the observed and predicted growth rates overlap in all cases, the point
estimates of the model predictions are usually higher than those observed from the monitoring program. It
is unclear whether the source of this bias is in the “working model's�� survival or reproductive process.
This model validation effort demonstrates the importance of considering a set of alternative models that
capture key uncertainties about population dynamics. Future modeling efforts should focus on the
following issues:
Reproduction.--Among eastern mallards, there is a strong negative relationship between fall age ratios and
indices of breeding-population size, suggesting a high degree of density dependence in reproduction. The
nature of this relationship is important because the presence of strong density-dependence in population
growth can lead to very liberal harvest strategies. Therefore, further investigations are needed to help
understand whether the observed relationship actually represents cause and effect. Also, questions remain
about the influence of environmental conditions on reproduction. To date, no weather variables have
explained much of the variation in fall age ratios, and it is unclear whether these results reflect an
insensitivity to weather conditions or a failure to identify the appropriate weather variable(s).
AHM for Eastern Mallards Page 11
The “working model” relies on the empirical relationship between population size and the BBS index to
predict reproductive success. This relationship currently is based on only seven data points, one for each
year in which both the BBS index and N are available. Although the BBS index and N are positively
correlated (P < 0.01), there is considerable uncertainty regarding the slope, intercept, and shape of this
relationship (Fig. 3). By using a combination of optimization and simulation procedures, I determined that
optimal regulations for eastern mallards are very sensitive to the predicted relationship between N and the
BBS index, particularly at low and high population levels. It is therefore essential that this relationship be
monitored and updated as often as possible.
Mallard population size
5.0e+5 7.5e+5 1.0e+6 1.3e+6 1.5e+6
BBS index
0
1
2
3
4
5
6
7
8
9
10
Fig. 3. The relationship between mallard population size and the Breeding Bird Survey (BBS) index. The dotted
line is the least-square regression and the solid lines are 95% confidence intervals for the mean.
Survival.--There is some evidence that female mallards in the eastern population are more vulnerable to
harvest than their midcontinent counterparts. However, it has been difficult to understand the spatial and
temporal patterns (if any) of harvest vulnerability because band-reporting rates for female mallards in
eastern North America are unknown. Until estimates of band-reporting rate are available, managers
perhaps should consider sex-specific harvest vulnerability as a key source of uncertainty in population
models for eastern mallards.
AHM for Eastern Mallards Page 12
IV. What is the status of necessary modifications to the decision-making
process?
Harvest-management objective(s).--The preliminary objective for eastern mallards is to maximize long-term
cumulative harvest. This objective is subject to change once the implications for average population
size, variability in annual regulations, and other performance characteristics are better understood. The
objective for midcontinent mallards is to maximize long-term cumulative harvest, subject to a population
goal of 8.7 million breeding birds. One of the difficulties in modifying the current AHM framework
involves combining the population-specific objectives into one objective function so that an aggregate
harvest strategy can be derived.
I currently am using an objective function which maximizes the aggregate harvest of both populations, but
devalues all regulatory decisions that result in the midcontinent population falling below goal. This
objective function helps ensure that the midcontinent population goal is not sacrificed for the sake of more
eastern mallard harvest. Much work remains, however, to understand the implications of various objective
functions, particularly on Flyway-specific regulations.
Augmentation of the decision criteria.--I have made considerable progress in augmenting the decision
criteria to include population and environmental variables relevant to eastern mallards. A recent
investigation involves the following scenario:
(1) population models which include the “working model” for eastern mallards, and current models
and associated likelihood weights for midcontinent mallards;
(2) explicit consideration of the eastern population when making a regulatory decision (i.e., decision
criteria to include population sizes of both midcontinent & eastern mallards, Canadian ponds, and
spring precipitation in the northeastern U.S.);
(3) one regulatory decision to apply to all Flyways;
(4) the current set of regulatory alternatives;
(5) deterministic harvest rates (i.e., expected mean harvest rates for both populations under the current
regulatory alternatives); and
(6) an objective function that maximizes the combined harvests of midcontinent and eastern mallards,
subject to the population constraint on midcontinent mallards.
The two “decision matrices” for midcontinent and eastern mallards were “blended” into one via an
optimization algorithm developed for this problem. Because the number of decision criteria has been
increased, the optimal strategy can no longer be displayed as a matrix, but must take the form of a table
(Table 4). Although comprehensive patterns of optimal regulations are hard to discern from the small
portion of the strategy reproduced in Table 4, it does appear that population size of eastern mallards and
spring precipitation in the Northeast can modify the nationwide regulatory decision for a given status of
midcontinent mallards. However, the effect is very small, presumably because the midcontinent population
is so numerically dominant.
AHM for Eastern Mallards Page 13
Table 4. Optimal regulations (C = closed, VR = very restrictive, R = restrictive, M = moderate, and L =
liberal) for mallards breeding in central and eastern North America. Only a small portion of the strategy is
contained in the table.
Midcontinent
population
(millions)
Ponds
(millions)
Eastern
population
(millions)
Northeast spring
precipitation
(inches)
Optimal
regulation
5.0 2.5 0.75 7 C
5.0 2.5 0.75 15 C
5.0 2.5 1.25 7 C
5.0 2.5 1.25 15 C
5.0 4..5 0.75 7 C
5.0 4.5 0.75 15 C
5.0 4.5 1.25 7 C
5.0 4.5 1.25 15 VR
6.5 2.5 0.75 7 VR
6.5 2.5 0.75 15 VR
6.5 2.5 1.25 7 VR
6.5 2.5 1.25 15 VR
6.5 4..5 0.75 7 R
6.5 4.5 0.75 15 R
6.5 4.5 1.25 7 R
6.5 4.5 1.25 15 M
8.0 2.5 0.75 7 M
8.0 2.5 0.75 15 M
8.0 2.5 1.25 7 M
8.0 2.5 1.25 15 M
8.0 4..5 0.75 7 L
8.0 4.5 0.75 15 L
8.0 4.5 1.25 7 L
8.0 4.5 1.25 15 L
AHM for Eastern Mallards Page 14
I compared this policy with the midcontinent policy from last year by taking the mean regulation over all
ponds, eastern mallard population sizes, and Northeast spring precipitation amounts for each level of
midcontinent population size (Fig. 4). For population sizes of midcontinent mallards >8.5 million, there is
little difference in regulations, suggesting that the status of eastern mallards has little effect on the
nationwide decision. At those levels, the midcontinent population simply dwarfs the eastern population
and, thus, dominates the choice of regulations. For midcontinent population sizes <6 million, explicit
consideration of eastern mallards will tend to produce more liberal regulations than would be the case with
a strategy focused solely on midcontinent mallards. In fact, for very low midcontinent mallard sizes,
consideration of eastern mallards can prevent a closed season from being the optimal choice. For
midcontinent population sizes between 6 and 8.5 million, the aggregate strategy actually appears to be
slightly more conservative than the strategy based on midcontinent mallards. I am not sure of the reason
for this result, but I suspect the conservative regulations permit more growth in the midcontinent
population, while substituting harvest from the eastern population. Thus, this example demonstrates the
importance of investigating the implications of various combinations of harvest management objectives for
midcontinent and eastern mallards.
Modification of the decision rules.--Modification of the decision rules to allow for Flyway-specific
regulatory choices greatly complicates the optimization procedures. Instead of five possible regulatory
decisions (C, VR, R, M, and L), we have to evaluate 54 = 625 decisions for every possible combination of
midcontinent population size, ponds, eastern population size, and spring precipitation in the Northeast. If
we assume that the Central and Pacific Flyways could share a regulatory decision, the number of decisions
could be reduced to 53 = 125. Although this simplification would be acceptable for now, the Central and
Pacific Flyways will require separate decisions if and when a western population of mallards is adopted.
The additional complexity arising from the expanded decision space will severely strain our computational
abilities. Investigations into computer hardware and software that can handle these large-dimension
problems are ongoing.
Although season length, bag limits, and other regulatory specifications always have been Flyway-specific,
liberalization or restriction of regulations usually has occurred concurrently in all Flyways. Because of this
tradition, our ability to predict harvest rates resulting from various combinations of Flyway-specific
regulatory alternatives is extremely limited. Therefore, it is imperative that we adopt a stable set of
regulatory alternatives, and then use those alternatives long enough to validate harvest rate predictions.
AHM for Eastern Mallards Page 15
Midcontinent population size
4.0e+6 5.0e+6 6.0e+6 7.0e+6 8.0e+6 9.0e+6 1.0e+7 1.1e+7 1.2e+7
Optimal regulation
0
1
2
3
4
midcontinent strategy
aggregate strategy
Fig. 4. Mean regulatory choices (0 = Closed, 1 = Very restrictive, 2 = Restrictive, 3 = Moderate, and 4 =
Liberal) for various levels of midcontinent population size, as based on the 1998 midcontinent mallard strategy
and on an aggregate strategy that also considers that status of eastern mallards.
AHM for Eastern Mallards Page 16
V. Are there any concerns about this effort?
The role of Flyway biologists.--There is a critical need for Flyway biologists to be involved in modeling the
population dynamics of eastern mallards, and in investigating the management implications of various
models and harvest-management objectives. The Office of Migratory Bird Management (MBMO) does not
have the necessary field experience to formulate hypotheses of eastern mallard ecology, nor does it have
adequate staff resources to sustain a unilateral modeling effort. I encourage the Atlantic Flyway Technical
Section to join in a working partnership, similar to the collaboration between MBMO and the Technical
Section's Canada Goose Committee. In that partnership, MBMO staff provide analytical tools and
assistance, but most investigations are conducted by the Canada Goose Committee.
Intermediate steps.--While we are making considerable progress, it is not yet clear when we will be ready
to move from a nationwide harvest strategy based on midcontinent mallards to a Flyway-specific approach
based on both midcontinent and eastern mallards. In the interim, two alternatives have been suggested.
The first involves augmenting the decision criteria to explicitly include population and environmental
variables relevant to eastern mallards, but continuing to permit only one regulatory decision for all
Flyways. The other alternative involves an Atlantic Flyway regulation based solely on eastern mallards,
and a regulatory choice for the other three Flyways based solely on midcontinent mallards. The first
alternative explicitly recognizes that there is a sharing of mallard populations among the Mississippi and
Atlantic Flyways. The second alternative assumes that there is little or no sharing of populations.
Although we know this assumption to be false, I believe this alternative likely poses little biological risk in
terms of mallard populations.
In the end, however, the problem comes down to predicting the harvest rates realized on each population
when Flyways select different regulatory alternatives. Otherwise, we have no basis to develop an optimal
strategy for either population (unless we assume eastern mallards don't go to the Mississippi Flyway, and
midcontinent mallards don't go to the Atlantic). Since there is a sharing of populations among the Flyways,
we must be able to predict these population-specific harvest rates, even if we were to let the Atlantic be
guided solely by the eastern population, and the rest of the country by the midcontinent population. If we
knew the harvest rates for various combinations of Flyway-specific regulations, then we could develop the
full-featured harvest strategy. Thus, we come full circle, and I believe that the first alternative described
above is the only possible intermediate step. However, the management community must judge whether
this intermediate step is necessary or desirable, given that the interim strategy appears to be only
marginally different from that for the midcontinent population.
Other species.--I am concerned that the “working model,” which tends to over-predict population size,
suggests a very liberal harvest strategy. I don't believe it would be prudent to formally adopt this model, or
its associated Flyway-specific strategies, without an explicit consideration of key sources of model
uncertainty, or without considering how the associated harvest strategy may impact the status of species
like black ducks, scaup, or wood ducks.